DMREF/Collaborative Research: Materials engineering of chromonic and colloidal liquid crystals via mathematical modeling and simulation

DMREF/合作研究：通过数学建模和模拟进行有色和胶体液晶的材料工程

• 批准号: 1434734
• 负责人: Amit Acharya
• 金额: $ 34.77万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1434734&HistoricalAwards=false
• 关键词: DMREF; Collaborative; Research; Materials; engineering

This research project is at the intersection of the fields of physics of nonlinear phenomena, applied mathematics, nonlinear analysis, and computation. Knowledge of liquid-crystal-based suspensions is currently advancing quite rapidly, motivated by applications in materials science as well as in biological systems. At a fundamental level, and in contrast with the disordered nature of normal suspending fluids, nematic order in a liquid crystalline matrix leads to long range elastic interactions either among colloidal particles or with bounding walls, resulting in a variety of unexpected phenomena. Furthermore, order in the matrix is distorted by the suspended particles, resulting in unavoidable topological defects that must move with the particles. On the one hand, the existence of structure in the liquid matrix affords new opportunities for flow control, processing, and suspension stability. At the same time, and for the same reasons, efficient engineering of these systems requires major advances to our current understanding of simple fluid colloids. From proposals for new display technologies and nanofluidic devices to more fundamental questions about the mechanisms of clustering and de-clustering in systems of particles, new experimental findings call for major modeling and analysis efforts. For example, studies of electrophoresis in structured media can facilitate related efforts in biology to model and control nano-fluidic transport as well as contribute towards understanding of motion of cancer cells and their clustering in tumor metastasis. This project addresses these important challenges through the formulation, analysis, and simulation of variational models of liquid crystalline colloids that allow for the presence of defects. Technology transfer is another component of the proposed research. Improved understanding of liquid crystal anchoring and defect dynamics will allow for higher resolution, faster display devices. The research aims to develop a predictive theory of transport in suspensions within an anisotropic liquid crystalline matrix, including electrostatically charged particles and ions. The particles can have arbitrary shapes, be rigid or soft, charged or electrically neutral, or be domains of the isotropic-nematic phase transition (chromonics). Analysis and computation will be used to explore both static and time dependent problems. Primarily variational methods will be employed, either within energy minimization for static problems or within the minimum dissipation principle for time dependent problems. Novel theoretical aspects include comprehensive models of colloidal systems in structured media that incorporate elasticity of the nematic matrix, surface anchoring, electric field, ions, and flow and their interplay. The relative importance of these effects will be established via the feedback between the modeling and experimental components of this project. A significant feature that determines the behavior of nematic liquid crystalline colloids is that the suspended particles are accompanied by topological defects in the nematic matrix. As singular structures, defects are inherently difficult to handle from a mathematical point of view, however they must be incorporated into any physically correct model. The principal challenge and contribution of the proposed work is formulation, analysis, and simulation of variational models of liquid crystalline colloids that allow for the presence of defects. Among the questions to be addressed are those of modeling of observed nonlinear electrophoresis and particle levitation, investigation of nematic domains in isotropic lyotropic chromonic liquid crystal, and modeling of the experimentally observed motion of disclination curves accompanied by negligible or no flow.

该研究项目处于非线性现象物理、应用数学、非线性分析和计算领域的交叉点。 受材料科学和生物系统应用的推动，基于液晶悬浮液的知识目前正在快速发展。 从根本上讲，与正常悬浮流体的无序性质相反，液晶基质中的向列顺序导致胶体颗粒之间或与边界壁之间的长程弹性相互作用，从而导致各种意想不到的现象。 此外，悬浮颗粒会扰乱基质中的秩序，导致不可避免的拓扑缺陷，这些缺陷必须与颗粒一起移动。 一方面，液体基质中结构的存在为流量控制、加工和悬浮稳定性提供了新的机会。 与此同时，出于同样的原因，这些系统的有效工程需要我们目前对简单流体胶体的理解取得重大进展。 从新显示技术和纳米流体设备的提议到有关粒子系统中的聚类和去聚类机制的更基本问题，新的实验结果需要进行重大的建模和分析工作。 例如，结构化介质中的电泳研究可以促进生物学领域的相关工作，以建模和控制纳米流体传输，并有助于理解癌细胞的运动及其在肿瘤转移中的聚集。 该项目通过允许缺陷存在的液晶胶体变分模型的制定、分析和模拟来解决这些重要的挑战。 技术转让是拟议研究的另一个组成部分。加深对液晶锚定和缺陷动力学的理解将有助于实现更高分辨率、更快的显示设备。该研究旨在开发一种各向异性液晶基质（包括带静电粒子和离子）内悬浮液传输的预测理论。 颗粒可以具有任意形状，可以是刚性的或软的，带电的或电中性的，或者是各向同性-向列相变的域（发色学）。 分析和计算将用于探索静态和时间相关问题。 将主要采用变分方法，无论是在静态问题的能量最小化内还是在时间相关问题的最小耗散原理内。 新颖的理论方面包括结构化介质中胶体系统的综合模型，其中包含向列基质的弹性、表面锚定、电场、离子和流动及其相互作用。 这些影响的相对重要性将通过该项目的建模和实验部分之间的反馈来确定。 决定向列液晶胶体行为的一个显着特征是悬浮颗粒伴随着向列基质中的拓扑缺陷。 作为奇异结构，从数学角度来看，缺陷本质上难以处理，但必须将它们纳入任何物理正确的模型中。 所提出的工作的主要挑战和贡献是允许缺陷存在的液晶胶体变分模型的制定、分析和模拟。 要解决的问题包括对观察到的非线性电泳和粒子悬浮进行建模、对各向同性溶致发色液晶中的向列域进行研究，以及对实验观察到的伴随着可忽略流动或无流动的向错曲线运动进行建模。